What data analysis is better? or fit for my data?
I've used Likert scale for my questionnaire (1-5) and I have 387 respondents.
Wilcoxon Rank Test or T-Test?
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A discrete variable with so few possible values can not be assumed to be distributed Gaussian, so you can't use t-test.
Also be careful using Wilcoxon tests, which one of signed-rank and rank-sum tests you have to choose depends on your data and question. If you are interested in whether median score is greater than/less than a specified value, you can use 1-sample Wilcoxon test, a slightly different approach to Wilcoxon signed-rank test. If your respondents are divided into 2 groups and you want to know whether median score of one group is greater than other one, you have to use Wilcoxon rank-sum test. If you have again 2 groups, but the respondents are somehow dependent, like they are siblings or same persons answering before and after some event, you have to use Wilcoxon signed-rank test. And if the respondents form more than 2 groups, you should consider Kruskal-Wallis test.